<i>T</i>-periodic solutions for some second order differential equations with singularities

Abstract

Synopsis We study the existence of T -periodic positive solutions of the equation where f ( t , .) has a singularity of repulsive type near the origin. Under the assumption that f ( t, x ) lies between two lines of positive slope for large and positive x , we find a non-resonance condition which predicts the existence of one T -periodic solution. Our main result gives a Fredholm alternative-like result for the existence of T -periodic positive solutions for